Coexistence of Magnetic Order and Two-dimensional
Superconductivity at LaAlO3/SrTiO3 Interfaces
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Citation
Li, Lu et al. “Coexistence of magnetic order and two-dimensional
superconductivity at LaAlO3/SrTiO3 interfaces.” Nature Physics
7.10 (2011): 762-766.
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http://dx.doi.org/10.1038/nphys2080
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Nature Publishing Group
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Author's final manuscript
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Thu May 26 04:51:41 EDT 2016
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http://hdl.handle.net/1721.1/72011
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Coexistence of Magnetic Order and Two-dimensional Superconductivity at LaAlO3/SrTiO3 Interfaces
1
2
2,3
Lu Li , C. Richter , J. Mannhart , R. C. Ashoori
1
1
Department of Physics, Massachusetts Institute of Technology,
Cambridge, Massachusetts 02139, USA
2
Center for Electronic Correlations and Magnetism,
University of Augsburg, 86135 Augsburg , Germany
3
Max Planck Institute for Solid State Research
70569 Stuttgart, Germany
A two dimensional electronic system forms at the interface between the band insulators1,2 LaAlO3
and SrTiO3. Samples fabricated until now have been found to be either magnetic or superconducting, depending on growth conditions3, 4. Combining high-resolution magnetic torque magnetometry
and transport measurements, we report here magnetization measurements providing direct
evidence of magnetic ordering of the two-dimensional electron liquid at the interface. The magnetic
ordering exists from well below the superconducting transition to up to 200 K, and is characterized
by an in-plane magnetic moment. Surprisingly, despite the presence of this magnetic ordering, the
interface superconducts below 120 mK. This is unusual because conventional superconductivity
rarely exists in magnetically ordered metals5, 6. Our results suggest that there is either phase
separation or coexistence between magnetic and superconducting states. The coexistence scenario
would point to an unconventional superconducting phase as ground state.
Superconductivity and magnetic order are in general mutually exclusive phenomena. Nonetheless, the
coexistence of magnetism and superconductivity has been suggested for finite momentum pairing states5, 6.
Coexistence of magnetism and superconductivity has been reported in a few 3D superconducting
systems7-9, such as RuSr2GdCu2O8 and UGe2. The question remains if such coexistence can occur in a
two-dimensional electronic system. An intriguing candidate is the interface between the two band
insulators LaAlO3 (LAO) and SrTiO3 (STO). At their n-type interface a conducting two-dimensional
electron liquid is generated. Moreover, the LAO/STO interface was also reported to have a 2D
superconducting ground state3.
For this system, magnetic ordering was suggested4 by Brinkman et al., who deduced the presence of
magnetic scattering centers from the temperature dependence of the interface resistance R and a hysteresis
of R during the sweep of magnetic field H. Different magnetotransport studies indicate an
antiferromagnetic order10 or a non-uniform field-induced magnetization and strong magnetic anisotropy11.
Recently, it was found that at both chemically treated STO bulk and LAO/STO interfaces, charges are
electronically phase separated into regions containing either a quasi-two-dimensional electron gas phase,
a ferromagnetic phase persisting above room temperature, or a diamagnetic/paramagnetic phase12 below
60 K. On the theoretical side, electronic structure calculations yield complicated pictures for the agnetism
at the interface layers13–16. Specifically, the calculations do not support magnetically ordered moments at
the interface of LAO/STO bilayer covered by vacuum17. Consequently, any observed magnetism must
originate from strong electronic correlations.
Coexistence of magnetism and superconductivity has not been reported at the LAO/STO interfaces. The
ground state was found to be controlled by growth conditions, carrier concentration18, and external
magnetic field19. These experimental observations based on transport properties suggest that the two
phenomena do not coexist (see, e.g., Fig. 16 of Ref.18).
To clarify this issue, we have grown LAO/STO interfaces, measured their superconducting properties by
transport measurements, and then applied cantilever-based torque magnetometry as an extremely sensitive
and direct method to measure a possible magnetic moment m of the sample.
Torque magnetometry directly determines m by measuring the torque τ of the sample mounted on a
cantilever in an external magnetic field H. As the torque is given by τ = m×B, the method detects the
component of m oriented perpendicular to B. Due to its great sensitivity, this method has been applied to
determine the magnetic susceptibility of very small samples, to analyze tiny magnetic signals, and, in
some cases, even to accurately map Fermi surfaces20–22.
In our setup, τ was measured with the sample glued to the tip of a 25 µm or 50 µm thick cantilever. H
was applied at a tilt angle ϕ with respect to the c-axis (perpendicular to the interface). The cantilever
deflection was detected capacitively. The moment m is given by m = τ/(µ0Hsinθ), where µ0 is the vacuum
o
permeability, and θ is the angle between m and H (with m in plane, θ = 90 −ϕ, see discussion below). We
used the measured angular dependence of the zero-field capacitance of the cantilever setup to calibrate the
spring constant of the cantilever. Knowing the spring constant, we quantitatively determine the value of m.
The cantilever setup can resolve changes22 in m of δm = 10
−13
- 10
−12
2
Am at 10 T.
All samples investigated were grown using nominally identical parameters for the substrate preparation
and the pulsed laser deposition. The films were patterned with Nb ohmic contacts and painted with silver
paste on the back. The only intended difference between the samples is that for one reference sample
(named “0 u.c.” sample), a shutter in front of the substrate was used to block the growth of LAO (Fig.
1(a)). The resistance of the interface samples was measured using the Nb ohmic contacts. The LAO/STO
interfaces were found to be superconducting below 120 mK. The superconducting temperature is slightly
lower than that of many other LAO/STO samples grown in the same condition, which might be the result
of unintended variations of growth parameters.
An example of the τ − H dependence is shown as the red curve in Fig. 1(b) for a 5 u.c. sample. The torque
signal has a pronounced reversible curve with a sharp “cusp” at low field. This cusp is displayed clearly
by Fig. 1(c), which zooms into this cusp. Fig. 1(d) shows m determined from the τ − H curve at -2 T ≤
µ0H ≤ 2 T. The V-shape of the τ − H curve centered at H =0 yields a nonzero, H-independent m for µ0H
up to 0.5 T. Close to H = 0, m jumps to 5 × 10
−10
2
Am , corresponding to 0.3 ~ 0.4 µB per interface unit cell
(assuming that the signal is generated by the STO unit cell next to the interface, see below). The values of
m very close to zero field (|µ0H| ≤ 5 mT) are hard to determine, because the small H causes a large
relative noise in m. At |µ0H| = 5 mT, δm ~ 4 × 10
−10
2
Am , which is close to the magnitude of m. Starting at
fields of order 1 Tesla, m diminishes gradually at higher H, suggesting that an additional contribution
appears in high fields. This high-field contribution was found to vary among different runs. Below we
focus on the low-field behavior.
To explore whether the torque signals originate from the LAO/STO interface, we performed control
experiments using reference samples. Sizable torque signals were only observed from samples containing
LAO/STO interfaces, the torque of which exceeds that of all background samples by two orders of
magnitude (Fig 1(b)). In particular, the superconducting Nb ohmic contacts are unlikely the source of the
torque signal, as the torque is found far above the upper critical field of Nb (0.4 T for bulk or 2 T for thin
films at 0 K). Moreover, all background m will be oriented closely parallel to H, thus creating small
torque responses only. The background m is also proportional to H, as these materials are paramagnetic or
diamagnetic. Furthermore, we measured a 5 u.c. thick LAO film grown on a LAO substrate. The torque
signal is again two orders of magnitude smaller than that of the 5 u.c. LAO/STO sample, excluding the
possible contribution from defects in the LAO film (see supplement). We therefore conclude that the
observed large torque indeed arises from the presence of the LAO/STO interface.
A chief motivation for our study was to determine whether the superconductivity and magnetic order
appear simultaneously or exist as separate phases in the T − H phase diagram. We observe that below the
superconducting Tc, the magnetic ordering signal and the superconducting state coexist. For the sample of
Fig. 2, for example, the superconducting transition occurs at 120 mK at H = 0, with a resistance foot
extending to 25 mK. The R − H curves measured at 20 mK with H parallel and perpendicular to the
interface plane are plotted in Fig. 2(b). While the interface is superconducting, the m − H curve at 20 mK
displays the same jump at small fields (Fig. 2(c)) as that observed at higher temperatures (Fig. 1(d)).
Notably, a finite m is recorded at µ0H ~ 5 mT, while the sample resistance R does not reach the normalstate value until µ0H ~ 20 mT. The magnetic ordering signal and the superconducting state are therefore
found to coexist.
The magnetic ordering signal is robust at elevated temperatures. For the 5 u.c. LAO/STO sample, m does
not show significant temperature dependence even up to 40 K (Fig. 3), the highest T at which this sample
was investigated. In another 5 u.c. LAO/STO sample, m was found to be nonzero up to 200 K (see
supplement). Such T - dependence is consistent with previous results12, reporting the existence of an
ordering state at room temperature. The high magnetic ordering temperature indicates a strong magnetic
exchange coupling.
The magnetic field dependence of m can be described by the Langevin-function characteristic for
superparamagnetism, where spins are aligned in small-size domains to behave as large classical magnetic
moments23. However, superparamagnetic samples usually show a strong temperature dependence in the
low-field m − H curves, a feature missing in the m − H curves in Fig. 3. Noise in our measurements of m
at fields close to zero may obscure this feature. Because m saturates at about 30 mT at T up to at least 40
3
K, the lower bound of the collective classical moment is around 10 µB. On the other hand, the m − H
curves are also consistent with a very soft ferromagnet whose hysteresis loop is hidden by the m noise at
|µ0H| < 5 mT. Although these two possibilities cannot be distinguished by our data, all of them suggest a
strong ferromagnetic-like magnetic coupling within domains.
To determine the orientation of the magnetic moment, we performed a series of torque measurements in
which the sample tilt angle was varied (see inset of Fig. 1(b)). Because τ = m × B = µ0mH⊥, where H⊥ is
the component of H perpendicular to m, the orientation of the moments can be discerned by tracking the
angular dependence of the torque signal. In highly anisotropic system, m is determined by H∥, the field
component parallel to m. Thus if H∥ is large enough to saturate m, τ will increase as a sine function of the
angle between H and m. On the other hand, once H∥ is insufficient to saturate m, τ will stop following the
sine behavior.
The angle-dependence shows that the saturation magnetic moment stays in the plane of the interface. We
carried out low-field torque measurements at 300 mK at 30 different tilt angles. Fig. 4 shows the τ − H
o
o
curves at several selected angles ϕ. As shown in Fig. 4(a), as ϕ changes from 15 to 94 , τ decreases
◦
monotonically and slowly approaches zero at ϕ = 90 , where H is almost parallel to m. On the other hand,
◦
◦
as ϕ varies between +15 and −10 , H is almost perpendicular to m. H∥ decreases and eventually changes
to the opposite direction. The in-plane magnetic moment drops to zero once H∥ is close to zero. As a
◦
◦
result, the τ(H) curves swing from a positive saturation at ϕ ~ 15 to a negative saturation at ϕ ~ -10 .
Our data show that 2D-superconductivity and magnetic order coexist at n-type LAO/STO interfaces. The
results leave the question open whether the same electrons are generating the superconducting and the
magnetic order. The measured results can be accounted for by scenarios of spatial phase separation, in
which inhomogeneous magnetic and superconducting electron layers are generated either in different
lateral puddles, or at different depths away from the interface. One possible cause of such
inhomogeneities is a non-uniform distribution of possible oxygen vacancies in the STO. This notion is in
accord with a proposal that the oxygen vacancies in the interfacial TiO2 layers stabilize ferromagnetictype order of the Ti ions close to the interface, as supported by DFT-calculations24. In this scenario the
superconducting phase is in close contact to the ferromagnetic phase, so the superconducting phase is
affected by the ferromagnetism. Furthermore, the data are also consistent with the idea that the same
electron system forms a magnetically ordered, superconducting electron liquid.
We note that, after our submission of the manuscript25, two experiments were reported to support the
coexistence of superconductivity and ferromagnetism at LAO/STO interface, based on hysteretic
magnetoresistance26, 27 and scanning SQUID imaging28.
In conclusion, using torque magnetometry we have performed quantitative measurements of the magnetic
moment of LAO-STO interfaces at wide-range magnetic field and broad temperature range, directly
showing the presence of magnetic order in the two-dimensional electron liquid of LAO/STO interfaces.
The order is characterized by a superparamagnetic-like behavior, with saturation magnetic moments of ~
0.3 µB per interface unit cell oriented in-plane, persisting beyond 200 K. Below 120 mK, the
ferromagnetic-like magnetic order and the 2D-superconductivity are coexisting.
Materials and Methods
The LaAlO3/SrTiO3 heterostructures were grown at the University of Augsburg using pulsed-laser
deposition with in-situ monitoring of the LaAlO3 layer thickness by reflection high-energy electron
diffraction. The single crystalline SrTiO3 substrates were TiO2 terminated. Their lateral size is 5 × 5 mm
2
−5
and their thickness is 1 mm. The LaAlO3 layers were grown at an oxygen pressure of 8 × 10 mbar at 780
o
C to a thickness of 5 u.c with a subsequent cooldown to 300 K in 0.5 bar of oxygen. The sputtered ohmic
Nb contacts filled holes patterned by etching with an Ar ion-beam. The reference (0 u.c.) samples were
−5
o
grown in the same conditions (oxygen pressure of 8 × 10 mbar at 780 C).
The magnetization measurements were preformed with a home-built cantilever-based torque
magnetometry apparatus at MIT. Cantilevers are made from thin gold or brass foils. We deposit gold film
on a sapphire and put it under the cantilever. The torque is tracked by measuring the capacitance between
the cantilever and the gold film, using a GR1615 capacitance bridge or an AH2700A capacitance bridge.
To calibrate the spring constant of the cantilever, we rotate the cantilever setup under zero magnetic field
to measure the capacitance change caused by the weight of the sample wafer.
Acknowledgement
The authors gratefully acknowledge helpful discussions with D. Grundler, T. Kopp, P. A. Lee, and G. A.
Sawatzky. This work was supported by ARO-54173PH, by the National Science Foundation through the
NSEC program, by the DFG (TRR 80), the EC (OxIDes), by DOE through the Basics Energy Sciences
program (FG02-08ER46514), and by the Nanoscale Research Initiative. L. Li would like to thank the
MIT Pappalardo Fellowships in Physics for their support. The high-field experiments were performed at
the National High Magnetic Field Laboratory, which is supported by NSF Cooperative Agreement No.
DMR-084173, by the State of Florida, and by the DOE.
Author contributions
The studies were designed, planned and analyzed by all authors, who also wrote the manuscript. C. R.
grew the samples, L. L. carried out the torque and resistivity measurements and the data analysis.
Correspondence and requests for materials should be addressed to R.A. (ashoori@mit.edu).
(a)
(b)
Sample 1 5 u.c. LaAlO3 on SrTiO3
H
φ
Nb ohmic contact
LaAlO3
SrTiO3
Ag back gate
Sample 2 0 u.c. LaAlO3 on SrTiO3
Nb ohmic contact
SrTiO3
Ag back gate
(d)
m
(c)
µ0H ( T )
µ0H ( T )
Fig. 1 Torque magnetometry of oxide interface LAO/STO. (Panel a) The schematics of an interface
sample (Sample 1) and of a 0 u.c. background sample (Sample 2), which were grown in the same
conditions. (Panel b) The field dependence of the torque curves of various test samples (cantilever only,
bare STO substrate, and the 0 u.c. sample) and a interface sample, taken at T = 300 mK and tilt angle ϕ ~
◦
15 . The inset shows a schematic of the cantilever setup. (Panel c) In Sample 1, a field dependence of the
torque curve is linear and symmetric below 0.5 T. (Panel d) In Sample 1, the magnetic moment m jumps
to a finite value within mT near zero field.
Fig. 2 Coexistence of superconductivity and magnetic ordering in a 5 u.c. LAO/STO interface
sample. (Panel a) The temperature T dependence of the resistance R shows a superconducting transition
at Tc = 120 mK. (Panel b) Field H dependence of R in different field directions taken at T = 20 mK.
◦
(Panel c) Field dependence of m measured at T = 20 mK at tilt angle ϕ ~ 15 away from the c-axis. The R
− H curve is also plotted with H parallel to the c-axis.
(a)
m
(b)
µ0H ( T )
µ0H ( T )
Fig. 3 Magnetic ordering persisting to elevated temperature. (Panel a) The torque vs. H curves of the
5 uc. LAO/STO sample measured at selected T between 300 mK and 40 K. Within the measurement noise,
no strong temperature dependence is observed. The title angle is about 49o. (Panel b) The curves of m vs.
H calculated from the torque curves.
(a)
(b)
φ
H
M
Fig. 4 Angular dependence of the interface torque suggesting an in-plane saturation magnetic
moment. At T = 300 mK, the magnetic torque of the 5 u.c. LAO/STO sample is measured at various tilt
angles φ between 15o and 94o (Panel a) and between -10o and 15o ( Panel b). The inset of Panel b shows
the geometry of the field H, magnetization M, and the definition of the tilt angle φ.
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